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Homework Help: Fundamental frequency of a wire wheel spoke

  1. Dec 16, 2016 #1
    1. The problem statement, all variables and given/known data
    The spoke of a wire wheel is 9.5 cm long, 3.5 mm in diameter, and under tension of 2100 N. The wire is made of steel of density 7860 kg/m3. When struck with a metal tool at its center, the spoke rings at its fundamental frequency. What is that frequency?

    2. Relevant equations
    λn.fn=v and velocity:v=sqrt(T/μ) , lemda λn=2L/n and L= length of string
    fn=n/2L . sqrt(T/μ)
    fundamental≡ the first mode ⇒ n=1
    μ is the linear mass and must be in kg/m so we must multiply our density by the area which is π.r^2

    3. The attempt at a solution
    μ=7860*π*(3.5*10^-3)^2=0.302 kg/m
    f=1/(2*9.5*10^-2) . sqrt(2100/0.302)
    f= 438.8 Hz
    but the answer is incorrect why??
  2. jcsd
  3. Dec 16, 2016 #2


    User Avatar

    Staff: Mentor

    I've changed your thread title to more accurately describe the particular problem. Please choose thread titles that are not too general.

    Were you given the radius of the spoke?
  4. Dec 16, 2016 #3
    Ah okay. Thanks very much. I used the diameter as a radius wrongly. :)
    Now it will be 877Hz which is the correct answer
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